Question

3. Three resistance of 12, 15 and 20 ohms are connected first in series and

then in parallel. What is the equivalent resistance in each case?​

Answer 1

Answer:-

• In series = 47$\bf\Omega.$

• In parallel = 5$\bf\Omega.$

Explanation:-

Given:-

• Three Resistors of 12, 15 and 20 ohm.

To Find:-

• The equivalent resistance in series.

• The equivalent resistance in parallel.

Formulae Used:-

In Series,

$\\ \orange{\longrightarrow\boxed{\pink{\bf R_{eq} = R_1+R_2+R_3...}}}$

In Parallel,

$\\ \orange{\longrightarrow\boxed{\pink{\bf \dfrac{1}{R_{eq}} = \dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}...}}}$

Where,

• Req = Equivalent Resistance.

• R1, R2 and R3... are given Resistors.

So Here,

• Req = ?? [to Find]

• R1, R2 and R3 = 12, 15 and 20 ohm respectively.

Case I:-

Resistors are connected in series:-

$\\ \mapsto\bf R_{eq} = R_1+R_2+R_3.$

$\\ \tt\mapsto R_{eq} = \bigg(12 + 15 + 20 \bigg) \Omega.$

$\\ \tt\mapsto R_{eq} = \bigg(12 + 35 \bigg) \Omega.$

$\\ \tt\mapsto R_{eq} =47 \Omega.$

Therefore in series combination equivalent resistance is 47 ohm.

Case II:-

Resistors are connected in series:-

$\\ \bf\mapsto \dfrac{1}{R_{eq }} = \frac{1}{R_1} + \frac{1}{R_2} +\frac{1}{R_3} .$

$\\ \tt\mapsto \dfrac{1}{R_{eq }} = \bigg(\frac{1}{12} + \frac{1}{15} + \dfrac{1}{20} \bigg)\Omega.$

$\\ \tt\mapsto \dfrac{1}{R_{eq }} = \bigg(\dfrac{(1 \times 5) + (1 \times 4) + (1 \times 3)}{60} \bigg) \Omega. \: \: \rm(taking \: lcm).$

$\\ \tt\mapsto \dfrac{1}{R_{eq }} = \bigg(\frac{5 +4 + 3 }{60} \bigg)\Omega.$

$\\ \tt\mapsto \dfrac{1}{R_{eq }} = \bigg( \cancel\frac{12}{60} \bigg)\Omega.$

$\\ \tt\mapsto \dfrac{ \cancel1}{R_{eq }} = \bigg(\frac{ \cancel1}{5} \bigg)\Omega.$

$\\ \tt\mapsto R_{eq} = 5 \Omega.$

Therefore in parallel combination equivalent resistance is 5 ohm.

Answer 2

Answer:

Explanation:

Given:-

Three Resistors of 12, 15 and 20 ohm.

To Find:-

The equivalent resistance in series.

The equivalent resistance in parallel.

Formulae Used:-

In Series,  

In Parallel,  

Where,  

Req = Equivalent Resistance.

R1, R2 and R3... are given Resistors.

So Here,

Req = ?? [to Find]

R1, R2 and R3 = 12, 15 and 20 ohm respectively.

Case I:-

Resistors are connected in series:-

Therefore in series combination equivalent resistance is 47 ohm.

Case II:-

Resistors are connected in series:-    

Therefore in parallel combination equivalent resistance is 5 ohm.